Kerr-Newman Black Hole Entropy and Soft Hair

TL;DR

The paper addresses reproducing Kerr–Newman black hole entropy through a horizon Virasoro/soft-hair framework by extending the hidden conformal symmetry analysis to charged rotating black holes. The authors generalize the Kerr construction by incorporating charge $Q$, using conformal coordinates, Virasoro vector fields, and covariant charges with a Wald–Zoupas counterterm, and find central charges $c_L=c_R=12J$ with independent left/right temperatures $T_L$ and $T_R$ that yield the entropy via the Cardy formula. They show the Kerr–Newman entropy matches the Bekenstein–Hawking area law $S_{BH} = \pi(r_+^2+a^2) = A/4$, preserving the universal horizon CFT description. The results support horizon microstate counting via soft hair for charged, rotating black holes and illustrate how charge relaxes a previous temperature constraint while maintaining the area law.

Abstract

Recently a set of diffeomorphisms were found which act nontrivially on the Kerr horizon and form a left-right pair of Virasoro algebras. Using the boundary formula for the associated central charge and assuming applicability of the Cardy formula to a putative dual CFT, the Bekenstein-Hawking entropy for the Kerr black hole was reproduced. In this paper, the addition of charge to the black hole is shown to require a minimal modification to this construction which then reproduces the Bekenstein-Hawking entropy for the Kerr-Newman black hole.